1 PM EST Valuation of a constant growth stoock Investors require a 17% rate of r
ID: 2790036 • Letter: 1
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1 PM EST Valuation of a constant growth stoock Investors require a 17% rate of return on Levine Company's stock (ie, 4-17%). a. What is its value if the previous dividend was Do-$3.50 and investors expect dividends to grow at a constant annual rate of (1)-2%, (2) 0, (3) 4%, or (4) i2%, Round your answers to two decimal places. (2) $ (3) $ (4) $ b. Using data from part a, what would the Gordon (constant growth) model value be if the required rate of r eturn was 15% and the expected growth rate were (1) 15% or (2) 20%, Are these reasonable results? I. The results show that the formula does not make sense if the required rate of return is equal to or less than the expected growth rate. It the results show that the formula does not make sense if the required rate of return is equal to or greater than the expected lli,-, results show that the formula makes sense if the required rate of return is equal to or less than the epocted growth rate. IV. The results show that the formula makes sense if the required rate of return is equal to or greater than the expected growth rate. V. These results show that the formula does not make sense if the expected growth rate is equal to or less than the required rate of return. Select c Is it reasonable to think that a constant growth stock could have g > I. It is not reasonable for a firm to grow indefinitely at a rate higher than its required return. 11. It is reasonable for a firm to grow indefinitely at a rate higher than its required retum. I11. It is not reasonable for a firm to grow even for a short period of time at a rate higher than its required return for a firm to grow indefinitely at a rate equal to its required return It is not reasonable for a firm to grow indefinitely at a rate lower than its required return. V. It is not r F8 F9Explanation / Answer
i) Value of stock = D0 * (1 + growth rate)/ (rate of return - growth rate)
= $3.5 * (1-0.02)/(0.17+0.02) = $18.05
ii) Value of stock = D0 * (1 + growth rate)/ (rate of return - growth rate)
= $3.5 * (1+0)/(0.17-0) = $20.59
iii) Value of stock = D0 * (1 + growth rate)/ (rate of return - growth rate)
= $3.5 * (1+0.04)/(0.17-0.04) = $28
iv) Value of stock = D0 * (1 + growth rate)/ (rate of return - growth rate)
= $3.5 * (1+0.12)/(0.17-0.12) = $78.4
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When rate of return is 15% and growth rate = 15% or 20%
i) Value of stock = D0 * (1 + growth rate)/ (rate of return - growth rate)
= $3.5 * (1+0.15)/(0.15 -0.15) = $3.5 * 1.15 /0 = infinity
ii) Value of stock = D0 * (1 + growth rate)/ (rate of return - growth rate)
= $3.5 * (1+0.2)/(0.15-0.2) = $3.5 * 1.2 / -0.05 = -$84
The formula of constant growth doesn't make sense if rate of return is equal or less than growth rate as value of stock can not be infinity or negative. Option 1 is correct
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Option 1 is correct. A firm cannot grow at rate higher than expected rate in perpetuity. It can grow for short periods at a rate higher than market rate but if that happens indefinitely than that would just make the firm the best investment ever and it will grow bigger than any market and any economy.
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